Beyond the classic role of radar to detect and measure the range to an object, and discriminate between objects, disclosed is a system and method to detect and use the different facts about the backscatter. These facts include: (1) whether or not nonlinear backscattered signals exist; (2) what the characteristics of the nonlinearity are, such as the shape of the nonlinear curvature and relative magnitudes and phases of 2nd, 3rd, 4th, 5th order terms etc.; (3) whether or not these nonlinear backscattered signals are modulated; and (4) characteristics of this modulation, such as characteristic features obtained using a joint-time-frequency analysis or wavelet analysis. The use of these facts allows the system and method to perform new functions. For example, the fact that the nonlinear backscatter is, or is not, modulated can be used to infer that the object causing the nonlinear backscatter is a piece of electrical equipment that is either operating (powered-on) or not. For another example, the modulation characteristics can be used to infer circuit state changes that allow classification of the type of target, such as a type of cell-phone or WiFi access point, or reading data that is driving those circuit states.
Nonlinear backscatter from an electronics device changes with any current or voltage that is applied to it by the circuit surrounding the device. Example devices include a diode, vacuum tube, bipolar junction transistor (BJT), junction field effects transistor (JFET), a metal-oxide-metal junction as occurs where rusted metal pieces or dissimilar metals contact each other, a metal-oxide-semiconductor (MOS) junction such as found in a MOSFET, and essentially all semiconductor devices used in electronic circuits. Therefore, a NLR can be used to measure or relate circuit conditions or states to modulation carried on the backscatter signal. The range at which a NLR can perform these detection, discrimination, and classification functions depend on its sensitivity and the nonlinear RCS and bandwidth of the target of interest.
Radar is the preeminent long-range day/night all weather (rain, dust, snow) “eyes and ears” of the human race. Modern radar systems must not only detect objects that reflect radio waves and measure their range, they must discriminate between different types of targets. In order to do this discrimination, modern radars have used six domains:                (1) radar cross section (RCS)—both the absolute and relative magnitudes of reflected energy are used to detect and discriminate between targets;        (2) multi-frequency backscatter metrics—the relative phase and magnitude of a target's backscatter at multiple frequencies is used to discriminate between different types of targets;        (3) polarimetry—which is used to infer orientation & shape metrics;        (4) high range resolution—which is used to get down-range profiles able to identify, for example, different trucks or aircraft by their range profile;        (5) high angular or cross-range resolution—which is obtained using both real or synthetic aperture beamforming to allow imaging and isolation of one target from another and identify targets by their image shape when combined with high range resolution;        (6) doppler measurement and analysis, both macro and micro—which is used to                    (a) discriminate between reflecting objects based on their speed, such as discerning extremely small targets that are moving within large stationary clutter (like a person walking in a forest),            (b) discern between and classify objects, or infer what mode they are operating in based on their vibrations, such as those linked with the spin-rate and number of blades used on a turbine or propeller, and            (c) discriminate between different objects by analyzing local motion, where examples include (i) inverse SAR (ISAR) such as where the motion of a ship superstructure swaying back and forth with the ocean waves, effectively rotating about the main hull, provides Doppler velocity that is proportional to height above the rotation center, and (ii) the limbs of a person swaying relative to the torso; and                        (7) nonlinear responses from targets containing junctions, like rusty chains with metal-oxide-metal junctions, or active electronics devices that have various kinds of semiconductor junctions, in order to discriminate between passive and active targets.        
“Unified Understanding of RF Remote Probing,” by John A. Kosinski, W. Devereux Palmer, Michael B. Steer, IEEE SENSORS JOURNAL, VOL. 11, NO. 12, December 2011 pp. 3055-3063 Steve C. Cripps, Advanced Techniques in RF Power Amplifier Design, 2002 Artech House, Norwood, Mass., 2002016427, ISBN 1-58053-282-9 is a recent overview of remote sensing technology that covers both linear and NLR. “Robust Analog Canceller for High-Dynamic-Range Radio Frequency Measurement,” by Wetherington, Joshua M.; Steer, Michael B., Microwave Theory and Techniques, IEEE Transactions on, vol. 60, no. 6, pp. 1709-1719, June 2012 is a recent book describing advanced power amplifier design techniques that address nonlinear behavior in power amplifiers. The author states on page 79 that “more focused effort should be directed at using two-carrier tests to derive polynomial models rather than single-carrier gain and phase sweeps.” The disclosed method does exactly that, it allows high resolution measurements of the parameters for a polynomial model. “A Vector Intermodulation Analyzer Applied to Behavioral Modeling of Nonlinear Amplifiers With Memory,” by Aaron Walker, Michael Steer, and Kevin G. Gard, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 5, May 2006, pp 1991-1999 is a recent article showing the extreme lengths that are taken to mitigate nonlinear behavior in a spectrum analyzer or receiver. The problem with the approach shown is that while it works for a highly control test apparatus, it does not work for a general radar problem where the backscatter signal picked up by the receiver is a high dynamic range random process due to the transmit signals interaction with random targets and clutter. The problem is that even as highly developed as radar has become in the domains of (1) to (6) listed in the previous paragraph, its ability to discriminate between active and passive targets (domain (7)) is not highly developed. Furthermore, the use of NLR to remotely collect information-bearing modulation on the nonlinear backscatter signal and use it to aid discrimination, classification, determination of circuit conditions, and to remotely receive data when the circuit conditions are modulated by data has not been done heretofore. While NLR has been used in specialty applications like tracking insects tagged with a tiny diode and wideband antenna, it has not been broadly applied to problems that have uncontrolled targets-of-opportunity. Adding better nonlinear capability promises to address a major shortfall with current radar systems—a high false alarm rate caused by an inability to discriminate between the particular objects of interest and the huge volume of undesired “clutter” objects using only the first five domains listed above.
The disclosed NLR addresses this shortfall and provides a huge reduction in fall alarms for a myriad of applications or uses. One of these uses is to quickly and reliably find improvised explosive devices (IEDs). IEDs are difficult to detect simply because they are surrounded by so much clutter. They are currently causing significant damage to US and allied forces. Disclosed is a system and method to bring nonlinear target behavior into radar's tool-kit of discriminators to quickly identify high priority man-made objects—objects that are hidden by a plethora of detects from both man-made and naturally occurring objects like rocks, trees, bumps in the terrain, buildings, rubble, etc.
A small but hard set of problems has caused previous NLR systems to fail to obtain the wide use that linear radar has enjoyed. The set of problems is summarized as problems (a)-(f) in the list below. From a phenomenology perspective, the key problems with even an ideal NLR are (1) that the received signal, in free space, power falls off in range (R) as a function of R8 (for the 3rd order term) as opposed to normal radar that falls off with R4, and (2) that the nonlinear radar cross section (NL-RCS) is much smaller than the normal body-size driven RCS. Together, these two factors drastically reduce the operational range of even an ideal, perfectly linear, radar.
These fundamental-physics drive realizations to high power levels, high receiver sensitivity, wide bandwidth, ultra high linearity and to be operationally feasible, a low size weight and power and cost (SWaP-C). To be more specific, a system must simultaneously addresses problems (a)-(f) listed below.                (a) On the receive side, the nonlinear (or harmonic) backscatter term is extremely small yet must be received in the presence of the large fundamental returns—a situation that requires extremely low noise and internally generated harmonics, or in other words, extremely high dynamic range from the receiver.        (b) On the transmit side, high transmit power is needed to illicit a large enough nonlinear backscatter to be measurable at an operationally useful range but at the same time, the transmitter's own spurious/harmonic emissions must be low enough that they don't cover-up the tiny nonlinear backscatter energy—a situation requiring extremely high linearity in the transmitter.        (c) In order to resolve targets at different ranges and not have nonlinear responses generated by targets a different ranges all pile on top of one another, wide bandwidths are needed—a situation that requires (a) and (b) to be done across wide bandwidths, making narrowband designs using deep stop-band narrowband filters unfeasible.        (d) Operational needs place strict limits on size weight and power and cost (SWaP-C), so regardless of how difficult it is to find a low SWaP-C solution for (a), (b), and (c), the solution must be low SWaP-C.        (e) The ultimate range resolution and operating range depends on target's nonlinear RCS and its bandwidth—a situation that requires (a), (b), (c), and (d) to be met in a system that must have modes constrained enough to work within the frequency ranges of the in-going and out-coming coupling coefficients of the target (i.e. getting power into a target at the fundamental frequencies, and the harmonic terms out at a different frequencies), and at the same time be flexible enough to work with a wide variety of targets with a wide variety of frequency ranges and bandwidths.        (f) Operational scenarios must permit shorter ranges and have reasonable target sets that recognize that even if we had an ideal radar, the R8 drop in power for an NLR versus R4 drop for a linear radar means that the NLR will never operate as far as normal radar.        
To illustrate problem (f), “Link budget calculations for nonlinear scattering,” by Fazi, C.; Crowne, F.; Ressler, M., Antennas and Propagation (EUCAP), 2012 6th European Conference on, vol., no., pp. 1146-1150, 26-30 Mar. 2012 gives an example case of a 1000 watt radar, where R0, the range where the received signal-to-noise-ratio (SNR) is 1, or 0 dB (i.e. the signal and noise powers match) was 320 km for the normal (linear) backscatter but only 2.7 km for the NLR using 3rd order backscatter.
Assuming the received power of the nonlinear response varies as R8 a receiver integration gain of 256 (24 dB) is required to double R0 to 5.4 km. At this range, the received signal is typically below the harmonic-noise-floor of the transmitter and receiver. As such, this 24 dB of integration would not work and would only reveal the radar's own nonlinearities. This integration cannot be done without a system and method that is either inherently more linearly than currently available, or that cancels nonlinear terms generated in the radar itself. Disclosed is an NLR that which can do either or both.
The difficulty of reducing nonlinear terms is particularly difficult for the receiver. The transmitter only needs to manage a few (one or two) signals—signals that are well known, repeatable, and under the designers control. The fact that there are few signals means that there are few and well-known nonlinear terms. The fact that so much is known, repeatable, and under the designer's control allows multiple techniques, circuit topologies, pre-distortion, and feedback loops to help linearize the transmitter. The receiver, on the other hand, is exposed to backscatter from a multitude of random targets of different sizes and at different angles and ranges. This backscatter sums to a diverse waveform with a high peak-to-average ratio. The time varying and high peak-to-average signal causes time varying nonlinear terms to be generated in the sensitive and wideband receiver circuits—e.g. low-noise-amplifier (LNA), mixers, gain control circuits, and analog-to-digital converters (ADC). These time varying nonlinear terms must be reduced or eliminated in order to allow integration of the desired nonlinear response of the target to achieve extended ranges.
Even if we assume an ideal wideband linear radar, (e) and (f) from above must address the fundamental-physics limitations. The solution to (e) and (f) is to choose a suitable target at a suitable range. For example, the IED detection application is ideal for NLR. An IED is only hard to detect because it is surrounded by so much similar looking clutter. An IED's nonlinear response may be instrumental in making it stand out from all the clutter surrounding it. Furthermore, the search area is relatively small since IEDs are placed close to known roadways or paths where vehicles that make attractive targets for IEDs travel. That being the case, the NLR can be positioned at a relatively short range. For example, trucks targeted by the IEDs could carry a modest size (˜100 watts, ˜1 m2 antenna) NLR. A low flying helicopter or airship could also carry the radar. If successful, such a radar would dramatically affect operations where IEDs are a threat. So part of the problem space is solved just by changing the scenario (range and target type). Clearly if the NLR could be made more sensitive, a broader application space could be covered.
As opposed to a general purpose NLR that must work with targets of opportunity, the insect tracking NLR solved (e) by making a custom tag (a custom target optimized to produce nonlinear backscatter) that guaranteed by design, good wideband coupling coefficients. The insect tracking radar that could transmit a single fundamental tone, f, and look for a 2nd order nonlinearity at twice the frequency of the fundamental, or 2f. It could also transmit two fundamental tones f1 and f2 and look for 2nd order terms of 2f1, 2f2, and f1+f2, which are generally larger than 3rd order terms of 2f1−f2, and 2f2−f1. The third order terms have the advantage that bandwidth of a resonant antenna can cover both the fundamentals and these 3rd order intermodulation products. But the 2nd order terms have the advantage that they are naturally stronger apart from the antenna affects.
In general, we will use the terms f1 and f2 to refer to the fundamental linear waveform terms that are transmitted (i.e. fundamental-1 and fundamental-2). Therefore, in some cases, f1 and f2 can refer to a tone at a frequency of f1 and f2 respectively, while in other cases, f1 and f2 can refer to two different wideband “fundamental” waveforms, such as a ramping-in-frequency chirp waveform, where f1 might have a different ramp-rate than f2.
Detecting targets that are well shielded and contain a radio, like a cell-phone or WiFi access point, for example, require energy to couple from some entry-point to the rest of the circuitry. In this case the entry-point could be a gap in the shield, or the antenna and filter circuits between the antenna and the rest of the circuitry, or the power cord and filters between the power cord and the rest of the circuitry. As opposed to the insect tracking system, this NLR must solve (e) by designing the transmitted and harmonic frequencies to pass through the entry-point's passband. In this case, a two-tone NLR would transmit fundamental frequencies of f1, f2, and fh represents a set of one or more harmonic terms to be received. Typically fh is the set {2f1−f2, 2f2−f1}. These two 3rd order terms have the property that they are close in frequency to f1 and f2. so that all these frequencies should be able to go through a common entry-point—a solution to (e) from above.
But that leaves problems (a)-(d). These problems are significant since the dynamic range required is beyond that achievable directly with standard wideband hardware. Even though narrowband architectures might provide the needed dynamic range by virtue of ultra-linear passive narrow bandwidth filters (such as LC, SAW, crystal, etc.), they fail at addressing (c) because their narrow bandwidth prevents them from providing the required radar range resolution. Even though ultra high linearity push-pull Class-A or Class AB amplifiers might be operated to give the needed low harmonic and spurious emissions, they fail to address (d) due to their extremely low efficiency at operating points that provide the required linearity.
Math Background
To briefly define a mathematical context, linear and nonlinear responses from objects illuminated by a transmitted signal st(t) can be modeled as a Taylor series expansion,
                                                        s              r                        ⁡                          (              t              )                                =                                    ∑                              i                =                1                            N                        ⁢                                          k                i                            *                                                s                  t                  i                                ⁡                                  (                  t                  )                                                                    ,                            (        1        )            
where sr(t) is the signal reflected by a particular target, st(t) is the transmitted signal, ki are the complex (real & imaginary or magnitude & phase) coefficients for the various powers, and where N sets the number of terms to be included in the expansion. The coefficients ki are the Taylor series coefficients that model the nonlinear curve that generates the nonlinear harmonics.
Taking the just the third order term (i=3) of a two tone signal, we find the following terms, amplitude coefficients, and phases:[a1*cos(2πf1t+θ1)+a2*cos(2πf2t+θ2)]3=(c1∠θ1)cos(2πf1t)+(c2∠θ2)cos(2πf2t)+(c3∠(2θ1−θ2))cos(2π(2f1−f2)t)+(c4∠(2θ2−θ1))cos(2π(2f2−f1)t)+(c5∠(2θ1+θ2))cos(2π(2f1+f2)t)+(c6∠(2θ2+θ2))cos(2π(2f2+f1)t)+(c7∠3θ1)cos(3f1)+(c8∠3θ2)cos(3f2)+  Equation (2)    c1=(3/4)*a13+(3/2)*a1*a22     c2=(3/2)*a12*a2+(3/4)*a23     c3=(3/4)*a12*a2     c4=(3/4)*a1*a22     c5=(3/4)*a12*a2     c6=(3/4)*a1*a22     c7=a13/4    c8=a23/4
Note that the output voltage is proportional to the cube of the input voltage for all terms, assuming the magnitude of both tones f1 and f2 are identical. For any particular order, the output frequencies are of the form n1f1+n2f2 where f1 and f2 are the tone frequencies, n1 and n2 are all possible integers and where the sum |n1|+|n2| is the order of the term. For example, at the fourth order (i.e.,[a1*cos(2πf1t+θ1)+a2*cos(2πf2t+θ2)]4),(|n1|, |n2|) & (|n2|, |n1|)ε{(0,2), (1,1), (0,4), (2,2), (1,3)} and the frequencies generated are: 2f1, f1+f2, f1−f2, 4f1, 2f1+2f2, 2f1−2f2, 3f1+f2, 3f1−f2, plus their symmetry pairs (symmetry meaning swapping f1 and f2 where it matters), 2f2, 4f2, 3f2+f1, 3f2−f1. As another example, at the fifth order, (|n1|, |n2|) & (|n2|, |n1|)ε{(0,1), (0,3), (1,2), (0,5), (1,4), (2,3)} and the frequencies generated are, f1, 3f1, f1+2f2, 2f1−f2, 5f1, 4f1+f2, 4f1−f2, 3f1+2f2, 3f1−2f2, and their symmetry pairs f2, 3f2, 2f1−f2, 2f2−f1, 5f2, 4f2+f1, 4f2−f1, 3f2+2f1, 3f2−2f1.Illustrative Measured and Simulated Backscatter Data
FIG. 1A is a circuit diagram of a nonlinear diode circuit model 100. As shown in FIG. 1A, the diode circuit 100 includes an AC voltage generator 110, a capacitance 120, a resistance 130, an inductance 140, a DC voltage generator 150, and a diode 160.
The AC voltage generator 110 generates an AC voltage VAC(t)=A(sin(2πf1t)+sin(2πf2t)), where A is a scaling factor, f1 is a first frequency, f2 is a second frequency, and t is time.
The capacitance 120 is connected between the AC voltage generator 110 and the resistance 130.
The resistance 130 is connected between the capacitance 120 and the diode 160.
The inductance 140 and the DC voltage generator 150 are formed in series, and this series circuit is connected in parallel with the diode 160.
The diode 160 is connected in series between the resistance 130 and ground. It is oriented so that current will flow from the resistance 130 to ground.
FIG. 1B the results of a SPICE (Simulation Program with Integrated Circuit Emphasis) simulation of the diode circuit 100 using an HSMS-286 Schottky diode as the diode 160. For this simulation, the amplitude of the AC voltage A=1V, f1=500 MHz, f2=510 MHz, C=20 pF, R=100Ω, L=4 μH, and VDC was set to supply a current of 0.1 μA.
FIG. 1B, shows first and second harmonics 170, 180. The first harmonics (or fundamentals) 170 centers around frequencies f1 and f2, while the second harmonic 180 centers around frequency (f1+f2).
FIG. 2 is a graph of the various harmonic levels versus the amplitude of the AC voltage, A, for the diode circuit 100 of FIG. 1. As shown in FIG. 2, there are harmonics at frequencies: f2 205, (f1+f2) 210, 2f1 215, (2f2−f1) 220, (3f2−2f1) 225, (4f2−3f1) 230, (5f2−4f1) 235, (3f1−f2) 240, (4f1−2f2) 245, and (5f1−3f2) 245.
FIG. 2 shows how the levels of various harmonic terms change with incident voltage. What the model cannot capture is the affect of coupling. Energy coupling can vary significantly across both wide and small frequency ranges. If we transmit frequencies f1 and f2, the coupling of each into a nonlinear component can be significantly different, and the coupling at the various nonlinear output frequencies can also be significantly different, not only across the wide frequency difference between a fundamental and its 2nd harmonic, but also between the f1, f2, 2f2−f1 and 2f1−f2 terms which are relatively close together. For applications like tracking a tag purposefully made to reflect nonlinear terms, like a zero-bias diode connected across an antenna, the 2nd order terms at double f1 and f2 and at f1+f2 are clearly the largest and easiest to detect terms. But if we want to detect a shielded radio, the energy must couple into the radio's circuits through an entry point like the antenna and any filter between the antenna and other circuits. In this case, there is a preference for both the illumination energy and the nonlinear reflected energy to be near the same frequency so both can travel through the entry point with low loss. This makes odd order terms like the 3rd order 2f1−f2 term and the 5th order 3f1−2f2 term of high interest.
Illustrative Measured Data Showing Nonlinearity of a State-of-the-Art E-PHEMT
FIGS. 3 through 8 illustrate state-of-the-art linearity and power efficiency in an E-PHEMT transistor amplifier. The data was measured on a MiniCircuits PHA-1+E-PHEMT amplifier that only draws 150 mA at 5 V (0.75 W) yet has a 42 dBm IP3 (3rd order intercept point) and 23 dB CP1 (1 dB compression point).
FIG. 3 is a graph 300 showing an adjacent channel leakage ratio (ACLR) versus output power 310 for the E-PHEMPT transistor amplifier. FIG. 4 is a graph showing error vector magnitude (EVM) versus output power for the E-PHEMPT transistor amplifier. In particular, FIG. 4 shows peak EVM versus output power 410, and average EVM versus output power 420.
ACLR and EVM are different metrics that measure linearity. The orthogonal frequency division multiplexing (OFDM) waveform sent to the amplifier is a sum of over 100 equal amplitude tones with a phase of 0, 90, 180, or 270 degrees chosen randomly across all the tones on a periodic basis. The resulting waveform has a high peak-to-average ratio which exercises nonlinearity in the amplifier. If the amplifier and test equipment were linear, there would be no energy in the adjacent channels. But at frequencies close to the fundamentals, the nonlinearity causes frequencies of (i+1)fk−ifj+(i+1)fj−ifk to be generated, where i equals integers from 1 to ∞, where N is the number of tones in the transmitted waveform, and where j≠k but otherwise j equals integers from 1 to N and k equals integers from 1 to N. Here, the order of the specific frequency term is 2i+1. These frequencies, being close to the fundamentals, land in adjacent channels. The ACLR measures the impact of nonlinearities because it is the nonlinearities that put energy in adjacent channels.
This high peak-to-average waveform that contains a large number of tones is similar to what the radar receiver circuits experience as they receive a myriad of copies of the transmitted signal delayed by a myriad of different times according to the range to the myriad of different objects. While it is important to manage the transmitter linearity, the fact that the receiver must cope with this high peak-to-average received waveform is why it is all the more important to manage the receiver linearity. The receiver does not have two well behaved tones with a modest 3 dB peak-to-average ratio like the transmitter, but instead, has a myriad of tones to interact nonlinearly. This high peak-to-average similarity is why the ACLR measurement is a good indicator of what the harmonic floor would be in a radar's receiver. The E-PHEMT amplifier described above was designed to provide exceptional ACLR relative to the power it consumes.
Note that at low output powers i.e. 6 dB or more below the 1-dB-compression-point (CP1), the ACLR degrades 4 dB per 1 dB increase in output power. Multiple techniques, both individually and in combinations, are typically applied in receivers to improve the linearity so that nonlinear terms produced in the receiver not to mask a received harmonic response from a target. These include simply running the amplifier far from its CP1 (i.e. high backoff), using multi-amplifier circuits (e.g. Doherty, balanced, etc), using pre-distortion circuits, and using circuit topologies with negative feedback. These techniques are effective for applications that have modest needs, like OFDM communications, because they work in a domain where they bring a severe nonlinearity down to a modest linearity, like −20 dBc harmonics down to −40 dBc. They do not work well, however, in a domain where nonlinear terms need to be over 90 dB down from the fundamentals, as is the case with NLR. High backoff is used on many OFDM systems due to their high peak-to-average-ratio (PAR). The E-PHEMPT amplifier mentioned above, with one of the best linearity-per-watt metrics available in today's technology, would meet a −100 dBc harmonic specification (or ACLR) at an output power of 0 dBm. Note that scaling this efficiency to a transmitter shows that doing so would require over 75 kilowatts of prime power to generate 100 W of RF power. These above facts illustrate the difficulty of solving problems (a)-(d) above.
FIG. 5 is a power spectrum plot, at an output power of 0 dBm, covering a desired channel, two adjacent channels below the desired channel, and two adjacent channels above the desired channel. The 0 dBm ACLR is simple the ratio of the power in this plot integrated over an adjacent channel relative to the power in this plot integrated over the desired channel.
FIG. 6 is a power spectrum plot, at an output power of 10 dBm, covering a desired channel, two adjacent channels below the desired channel, and two adjacent channels above the desired channel. This plot is used to compute the 10 dBm ACLR.
FIG. 7 is a power spectrum plot, at an output power of 15 dBm, covering a desired channel, two adjacent channels below the desired channel, and two adjacent channels above the desired channel. This plot is used to compute the 15 dBm ACLR.
FIG. 8 is a power spectrum plot, at an output power of 18 dBm, covering a desired channel, two adjacent channels below the desired channel, and two adjacent channels above the desired channel. This plot is used to compute the 18 dBm ACLR.